For private room conversations, there are no correct answers, but you have more interesting responses for these (at least the ones I’ve seen):
1st week – 3rd option (Why are you so imperious?)
2nd week – 3rd option (A beloved idol)
She’ll give you an Elixir after you have 100 battles with no damage (Perfect Battles)

Saber’s identity is Nero Claudius Caesar Augustus Germanicus, the Fifth Roman Emperor. She had the reputation of a notorious tyrant whose rule was made up of schemes and poison as she oppressed all religious forces, especially Christians, and the Roman Senate during the period from 50 to 60 AD.
Her Noble Phantasm is Aestus Domus Aurea